On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits

The Bell-Kochen-Specker theorem (BKS) theorem rules out realistic {\it non-contextual} theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the geometrical structure of small $v-l$ BKS-proofs involving $v$ real rays and $l$ $2n$-dimensional bases of $n$-qubits ($1< n < 5$). Specifically, we look at the parity proof 18-9 with two qubits (A. Cabello, 1996), the parity proof 36-11 with three qubits (M. Kernaghan & A. Peres, 1995 \cite{Kernaghan1965}) and a newly discovered non-parity proof 80-21 with four qubits (that improves work of P. K Aravind's group in 2008). The rays in question arise as real eigenstates shared by some maximal commuting sets (bases) of operators in the $n$-qubit Pauli group. One finds characteristic signatures of the distances between the bases, which carry various symmetries in their graphs.Comment: version to appear in European Physical Journal Plu

Immunomodulatory effect of xylazine, an alpha(2) adrenergic agonist, on rat spleen cells in culture

Xylazine is an adrenergic alpha (2) agonist, which is used in veterinary medicine as a sedative and anesthetic agent. In this work we found that xylazine administered in vivo at a dose of 2.5 mg/kg enhanced spleen cell proliferation and interleukin 2 (IL-2) production in cultures stimulated with concanavalin A (Con A), whereas doses of 10 and 25 mg/kg were inhibitory. A similar stimulatory (10 muM) and inhibitory (50-500 muM) effect on splenocyte proliferation and IL-2 production was observed in vitro. Clonidine. another alpha (2) adrenergic agonist, only had a stimulatory proliferative effect on splenocytes. Yohimbine, an alpha (2) adrenergic antagonist, abrogated the stimulatory action of both clonidine and xylazine, but not the suppressive proliferative activity of xylazine in vitro. The inhibited proliferation of splenocytes to Con A correlated with increased apoptosis of T cells. The apoptosis was not blocked by yohimbine or antibodies to Fas and Fas-L. N-Nitro-L-arginine methyl ester (L-NAME), an inhibitor of nitric oxide (NO) synthase. enhanced proliferation of splenocytes to Con Al partly abrogated the inhibitory effect of xylazine in the proliferation assay. and, only at high concentration (1000 muM), partly suppressed apoptosis of lymphocytes. The enhancing effect of L-NAME on the Con A-induced proliferation of splenocytes correlated with decreased NO production. However, decreased NO production observed in cultures with xylazine was followed by both decreased lymphocyte proliferation and apoptosis. Cumulatively, these results suggest that the immunosuppressive properties of xylazine on splenocytes in vitro are due to increased apoptosis of lymphocytes, predominantly involve NO-independent pathways, and are probably independent of its action through alpha (2) adrenoreceptors

Xylazine, an alpha(2)-adrenergic agonist, modulates proliferation of rat thymocytes in vivo and in vitro

The effect of xylazine, an alpha (2)-adrenergic agonist, on proliferation of rat thymocytes in vivo and in vitro was examined. It was found that the agonist administered to rats in vivo at doses of 2.5 mg/kg and 5 mg/kg stimulated thymocyte proliferation to suboptimal (0.625 mug/ml) concentrations of concanavalin A (Con A). A similar effect was confirmed in vitro when lower concentrations of xylazine (5 muM) were added to cultures of thymic cells from intact animals in the presence of both suboptimal and optimal (2.5 mug/ml) Con A concentrations. Higher doses in vivo (25 mg/kg) and in vitro (50 muM, 100 muM and 250 muM) significantly inhibited proliferation of thymocytes to Con A. The phenomenon was followed by a decrease in interleukin-2 (IL-2) production (in vivo and in vitro) and down-regulation of IL-2 receptor alpha (IL-2R alpha) expression (in vitro). The exogenous IL-2 completely restored the inhibitory effect of xylazine in vivo was observed. Stimulatory effect of xylazine on proliferation of thymocytes was probably mediated through alpha (2)-adrenoreceptors since it was blocked by yohimbine, an alpha (2)-adrenoreceptor antagonist. It seems that the pathways involved in inhibition of thymocyte proliferation by xylazine are more complex because the xylazine-suppressed thymocyte proliferation was potentiated by yohimine